If your web site is well designed to standards and is relevant to a topic searched, then you should be okay.
I strongly disagree on this point.
With good SEO, you can target key phrases and see your website appear for those key phrases, on the front page of google.
I do not believe that it is possible for the above to be achieved without any "forced" SEO work.
A removals company, which I work for, pays £360 to a company called Web360 and they work on moving our website up the rankings for certain key phrases. They even offered us a first month satisfaction guarantee (which is what initially tweaked our interest). Needless to say, they delivered on their promises in the first month and we have been paying them every month. I think they promised to get 70% of the key phrases we gave them, onto page 1 of google.
My advice would be to try speaking to different SEO companies and see if they give you a money back guarantee (on the first month). If they are confident on what they promise, they will put their money where their mouth is. You do not want to be in a position where they charge you £x and you see no improvement on your search engine rankings.
Another alternative is to use sponsored advertising on Google (or your favourite search engine). You have to run through the costs of using adverts vs SEO (organic search rankings) and use whichever works best for you. We tried using advertising, but found it more cost-effective to spend the money on SEO services and go for high rankings on organic searches.
Anyway...good luck.